In Othello, what are some examples about true and false ?
There are lots of possibilities here. Let's look at the mysogynist Iago who is true to his word shared with the audience that he will destroy his master Othello and Othello's innocent wife Desdemona-
I'll pour this pestilence into his ear—
That she repeals him for her body's lust;
And by how much she strives to do him good,
She shall undo her credit with the Moor.
So will I turn her virtue into pitch.
Iago has convinced himself that his actions are a just revenge for an indiscretion rumoured between his wife Emilia and Othello -
I do suspect the lusty Moor
Hath leap'd into my seat; the thought whereof
Doth (like a poisonous mineral) gnaw my inwards;
And nothing can or shall content my soul
Till I am evened with him, wife for wife.
Iago is true to his word and destroys everyone in this scenario: Othello, Desdemona and Emilia. In every other respect, Iago is a complete false 'Janus' deceptive to whomever he meets: his social contacts (Roderigo his friend); family ties (Emilia his wife); direct employer (Othello); colleague (Cassio) and the one innocent of his methods and undeserving of his hate--Desdemona.